SOLUTION: i did this problem i just want to see if i did it right.. what is the domain? 7-X/5x^2-18x-8 thanks for your help angela

Algebra ->  Functions -> SOLUTION: i did this problem i just want to see if i did it right.. what is the domain? 7-X/5x^2-18x-8 thanks for your help angela      Log On


   

Question 132287This question is from textbook introductory and intermediate algebra
: i did this problem i just want to see if i did it right..

what is the domain?
7-X/5x^2-18x-8

thanks for your help
angela This question is from textbook introductory and intermediate algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%287-x%29%2F%285x%5E2-18x-8%29 Start with the given function


5x%5E2-18x-8=0 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.




%28x-4%29%285x%2B2%29=0 Factor the left side (note: if you need help with factoring, check out this solver)




Now set each factor equal to zero:

x-4=0 or 5x%2B2=0

x=4 or x=-2%2F5 Now solve for x in each case


So our solutions are x=4 or x=-2%2F5



Since x=-2%2F5 and x=4 make the denominator equal to zero, this means we must exclude x=-2%2F5 and x=4 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x%3C%3E-2%2F5 or x%3C%3E4

So our domain looks like this in interval notation


note: remember, the parenthesis excludes -2%2F5 and 4 from the domain



If we wanted to graph the domain on a number line, we would get:

Graph of the domain in blue and the excluded values represented by open circles

Notice we have a continuous line until we get to the holes at x=-2%2F5 and x=4 (which is represented by the open circles).
This graphically represents our domain in which x can be any number except x cannot equal -2%2F5 or 4